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Growing through chaotic intervals

Author

Listed:
  • Gardini, Laura
  • Sushko, Iryna
  • Naimzada, Ahmad K.

Abstract

We consider a growth model proposed by Matsuyama [K. Matsuyama, Growing through cycles, Econometrica 67 (2) (1999) 335-347] in which two sources of economic growth are present: the mechanism of capital accumulation (Solow regime) and the process of technical change and innovations (Romer regime). We will shown that no stable cycle can exist, except for a fixed point and a cycle of period two. The Necessary and Sufficient conditions for regular or chaotic regimes are formulated. The bifurcation structure of the two-dimensional parameter plane is completely explained. It is shown how the border-collision bifurcation leads from the stable fixed point to pure chaotic regime (which consists either in 4-cyclical chaotic intervals, 2-cyclical chaotic intervals or in one chaotic interval).

Suggested Citation

  • Gardini, Laura & Sushko, Iryna & Naimzada, Ahmad K., 2008. "Growing through chaotic intervals," Journal of Economic Theory, Elsevier, vol. 143(1), pages 541-557, November.
    • Handle: RePEc:eee:jetheo:v:143:y:2008:i:1:p:541-557
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    References listed on IDEAS

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    1. Sushko, Iryna & Agliari, Anna & Gardini, Laura, 2006. "Bifurcation structure of parameter plane for a family of unimodal piecewise smooth maps: Border-collision bifurcation curves," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 756-770.
    2. Kiminori Matsuyama, 1999. "Growing Through Cycles," Econometrica, Econometric Society, vol. 67(2), pages 335-348, March.
    3. Anjan Mukherji, 2005. "Robust cyclical growth," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(3), pages 233-246, September.
    4. Mitra, Tapan, 2001. "A Sufficient Condition for Topological Chaos with an Application to a Model of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 133-152, January.
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